(13/3)a=6

Solution for (13/3)a=6 equation:

(13/3)a=6

We move all terms to the left:

(13/3)a-(6)=0


Domain of the equation: 3)a!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

(+13/3)a-6=0

We multiply parentheses

13a^2-6=0

a = 13; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·13·(-6)
Δ = 312
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{78}}{2*13}=\frac{0-2\sqrt{78}}{26}
=-\frac{2\sqrt{78}}{26}
=-\frac{\sqrt{78}}{13}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{78}}{2*13}=\frac{0+2\sqrt{78}}{26}
=\frac{2\sqrt{78}}{26}
=\frac{\sqrt{78}}{13}
$